It was perfect weather for hopping into bed, in public, with a total stranger. On Friday afternoon, the temperature was a glorious 75, and the water was glittering off Pier 45 in Hudson River Park.

Out past the water taxi stand and the sunbathers on the lawn, the Buenos Aires artist Fernando Rubio is making his American debut with a dreamy piece of pillow-talk theater called “Everything by my side.” A meditation on memory, written and directed by Mr. Rubio, it plays out on seven double beds widely spaced along the railing, stretching out to the tent at the end of the pier.

Lying on one side of each bed, under pristine white linens, is an actress in pale loungewear. Lying on the other is the audience: a single member of the public, shoes off, following — you hope — the preshow instruction to remain silent throughout. A group of seven experiences the show every 15 minutes.

Presented by Performance Space 122, Hudson River Park and the French Institute Alliance Française, “Everything by my side” is part of the Crossing the Line festival. It clearly crosses lines, including those of language, with performances in English and Spanish.

Looking like an art installation, it fits comfortably into the trend of immersive, one-on-one theater, but it also feels like performance art. Its very public-ness seems to demand from participants the kind of exhibitionism that Marina Abramovic asked of those who faced off with her at the Museum of Modern Art in 2010.

But amid the clamor of downtown Manhattan, Mr. Rubio has created seven little islands of intimacy. The actress in the bed I climbed into was Kate Douglas, and she didn’t say a word for quite a while after I lay down.

When she did speak, her voice was clear but soft, and she didn’t look at me — not at first, anyway. She spoke of a waking nightmare, of dreams of the future, of disappointment and disillusion, of resting in the moment.

“We’ll be here all weekend,” the people at the sign-in table were telling curious passers-by. The weather is supposed to be lovely. If you can, give it a try.